"Would something else be more effective?"
Yes, unless a shop is truly open to self-assign it should be labeled as apply.
There is nothing wrong with apply. If you meet all the criteria you can then be brought immediately to "you qualify for self-assign."
Today I had to cancel an application after waiting days to be assigned. The reason I was willing to do the shop was I could pick the place and the day. But it wasn't really self-assign. It was frustrating to be a bit mislead.
I guess I should have immediately cancelled my "application" rather than wait so long but you really don't know if it will be a few minutes or days for your application to be accepted or rejected. At this point my shop day has changed enough that I no longer am going to plan on doing that shop.
All lessons learned, I guess. Maybe commenting about it will help those making the word choices on the software understand a shoppers perspective a bit.
For those who always want to blame the shoppers, it's okay, I already take it. (But words do matter.)